On the 1/f Frequency Noise in Ultra-Stable Quartz Oscillators

The frequency flicker of an oscillator, which appears as a 1/f^3 line in the phase noise spectral density, and as a floor on the Allan variance plot, originates from two basic phenomena, namely: (1) the 1/f phase noise turned into 1/f frequency noise via the Leeson effect, and (2) the 1/f fluctuation of the resonator natural frequency. The discussion on which is the dominant effect, thus on how to improve the stability of the oscillator, has been going on for years without giving a clear answer. This article tackles the question by analyzing the phase noise spectrum of several commercial oscillators and laboratory prototypes, and demonstrates that the fluctuation of the resonator natural frequency is the dominant effect. The investigation method starts from reverse engineering the oscillator phase noise in order to show that if the Leeson effect was dominant, the resonator merit factor Q would be too low as compared to the available technology.Comment: 20 pages, list of symbols, 1 table, 6 figures, 43 reference

Characterization of Zero-Bias Microwave Diode Power Detectors at Cryogenic Temperature

We present the characterization of commercial tunnel diode low-level microwave power detectors at room and cryogenic temperatures. The sensitivity as well as the output voltage noise of the tunnel diodes are measured as functions of the applied microwave power, the signal frequency being 10 GHz. We highlight strong variations of the diode characteristics when the applied microwave power is higher than few microwatt. For a diode operating at ${4}$ K, the differential gain increases from ${1,000}$ V/W to about ${4,500}$ V/W when the power passes from ${-30}$ dBm to ${-20}$ dBm. The diode present a white noise floor equivalent to a NEP of ${0.8}$ pW/ ${\sqrt{\mathrm{Hz}}}$ and ${8}$ pW/${ \sqrt{\mathrm{Hz}}}$ at 4 K and 300 K respectively. Its flicker noise is equivalent to a relative amplitude noise power spectral density ${S_{\alpha}(1~\mathrm{Hz})=-120}$~dB/Hz at ${4}$ K. Flicker noise is 10 dB higher at room temperature.Comment: 8 pages and 16 figure

Tests of Sapphire Crystals Produced with Different Growth Processes for Ultra-stable Microwave Oscillators

We present the characterization of 8-12 GHz whispering gallery mode resonators machined in high-quality sapphire crystals elaborated with different growth techniques. These microwave resonators are intended to constitute the reference frequency of ultra-stable Cryogenic Sapphire Oscillators. We conducted systematic tests near 4 K on these crystals to determine the unloaded Q-factor and the turnover temperature for whispering gallery modes in the 8-12 GHz frequency range. These characterizations show that high quality sapphire crystals elaborated with the Heat Exchange or the Kyropoulos growth technique are both suitable to meet a fractional frequency stability better than 1x10-15 for 1 s to 10.000 s integration times.Comment: 7 figure

DC-powered Fe3+:sapphire Maser and its Sensitivity to Ultraviolet Light

The zero-field Fe3+:sapphire whispering-gallery-mode maser oscillator exhibits several alluring features: Its output is many orders of magnitude brighter than that of an active hydrogen maser and thus far less degraded by spontaneous-emission (Schawlow-Townes) and/or receiving-amplifier noise. Its oscillator loop is confined to a piece of mono-crystalline rock bolted into a metal can. Its quiet amplification combined with high resonator Q provide the ingredients for exceptionally low phase noise. We here concentrate on novelties addressing the fundamental conundrums and technical challenges that impede progress. (1) Roasting: The "mase-ability" of sapphire depends significantly on the chemical conditions under which it is grown and heat-treated. We provide some fresh details and nuances here. (2) Simplification: This paper obviates the need for a Ka-band synthesizer: it describes how a 31.3 GHz loop oscillator, operating on the preferred WG pump mode, incorporating Pound locking, was built from low-cost components. (3) "Dark Matter": A Siegman-level analysis of the experimental data determines the substitutional concentration of Fe3+ in HEMEX to be less than a part per billion prior to roasting and up to a few hundred ppb afterwards. Chemical assays, using different techniques (incl. glow discharge mass spectra spectroscopy and neutron activation analysis) consistently indicate, however, that HEMEX contains iron at concentrations of a few parts per million. Drawing from several forgotten-about/under-appreciated papers, this substantial discrepancy is addressed. (4) Excitons: Towards providing a new means of controlling the Fe3+:sapph. system, a cryogenic sapphire ring was illuminated, whilst masing, with UV light at wavelengths corresponding to known electronic and charge-transfer (thus valence-altering) transitions. Preliminary experiments are reported.Comment: pdf only; submitted to the proceedings of the 24th European Frequency and Time Forum, 13-15th April, 201

On the degeneracy of whispering gallery modes in a high-Q sapphire microwave resonator

Cylindrical WGM resonators machined in high-quality sapphire monocrystal cooled down to liquid helium temperature offer exceptionally-high Q-factors in the microwave frequency domain. Such a resonator constitutes the core of an ultra-stable oscillator featuring fractional frequency stability better than 1e-15 at short integration times. As in any cylindrical resonant structure, the WGM resonator presents a two fold degeneracy. When a defect breaks the cylindrical symmetry of the resonator, the WGMs split and appear as doublets. In the high-quality sapphire resonator, the frequency separation of these twin modes varies from one mode order to another with a maximum value of a few tens of kHz. While the mode splitting for a given mode was considered until now unpredictable and intrinsic to each resonator since resulting a priori from randomly distributed defects. we show here, at the contrary, that the observed mode splitting found on all the sapphire resonators whatever their origin mainly comes from a perfectly determined defect resulting from the manufacturing processes.Comment: 7 pages, 10 figure

Influence of the ESR saturation on the power sensitivity of cryogenic sapphire resonators

Here, we study the paramagnetic ions behavior in presence of a strong microwave electromagnetic field sustained inside a cryogenic sapphire whispering gallery mode resonator. The high frequency measurement resolution that can be now achieved by comparing two CSOs permit for the first time to observe clearly the non-linearity of the resonator power sensitivity. These observations that in turn allow us to optimize the CSO operation, are well explained by the Electron Spin Resonance (ESR) saturation of the paramagnetic impurities contained in the sapphire crystal.Comment: 8 pages, 9 figure

Compact Yb+^+ optical atomic clock project: design principle and current status

We present the design of a compact optical clock based on the $^2S_{1/2} \rightarrow ^2D_{3/2}$ 435.5 nm transition in $^{171}$Yb$^+$. The ion trap will be based on a micro-fabricated circuit, with surface electrodes generating a trapping potential to localize a single Yb ion a few hundred $\mu$m from the electrodes. We present our trap design as well as simulations of the resulting trapping pseudo-potential. We also present a compact, multi-channel wavelength meter that will permit the frequency stabilization of the cooling, repumping and clear-out lasers at 369.5 nm, 935.2 nm and 638.6 nm needed to cool the ion. We use this wavelength meter to characterize and stabilize the frequency of extended cavity diode lasers at 369.5 nm and 638.6 nm.Comment: 7 pages, 5 figures. Proc. of the 8th FSM 2015, Potsdam, Germany. To be published in IOP Journal of Physics: Conference Serie

Bruit des oscillateurs et des résonateurs à quartz

Un des problèmes qui se posent au concepteur des oscillateurs à quartz de haute stabilité est le bruit propre des résonateurs. Nous effectuons tout d'abord une brève description des principaux mécanismes susceptibles d'affecter la stabilité des oscillateurs et des résonateurs à quartz. Ensuite sont explicitées les grandeurs mises en jeu dans la métrologie des fréquences : la densité spectrale de bruit de phase dans le domaine spectral et la variance d'Allan dans le domaine temporel. Enfin nous présentons l'instrumentation utilisée et développée pour la mesure du bruit des oscillateurs en général et des résonateurs en particulier